CN115361118A - Loss tolerant reference frame and measuring device independent quantum key distribution method - Google Patents

Abstract

The invention relates to a method for distributing independent quantum keys of a reference system and a measuring device with loss tolerance.

Description

Loss tolerant reference frame and measuring device independent quantum key distribution method

Technical Field

The invention belongs to the field of quantum key distribution, and particularly relates to a method for distributing a quantum key independent of a reference system and a measuring device with loss tolerance.

Background

Quantum cryptography is one of the practical applications that stems from quantum mechanics. By employing unconditionally secure "one-time-pad" encryption algorithms, quantum cryptography can shift the security of encryption into key distribution, which is also referred to as Quantum Key Distribution (QKD). Since the first protocol was proposed in 1984, QKD has had a vigorous development, both in theoretical and experimental terms, to deal with practical imperfections. In continuous development, a spoofing method and a measuring device independent protocol (MDI QKD) fill the major vulnerabilities of a transmitting end and a receiving end, respectively, and are widely applied to QKD systems and networks.

Meanwhile, in practical implementation, the QKD based on polarization or phase encoding needs to be calibrated in real time to keep the system stable. To address this time consuming and complex requirement, the relevant scholars have proposed a reference frame independent protocol (RFI QKD) and a protocol independent of both the reference frame and the measurement device (RFI-MDI QKD). The current research situation makes great progress in protocol optimization and system demonstration, especially for RFI-MDI QKD protocol, which inherits the high security of MDI protocol and is also verified in long transmission distance.

But in addition, eavesdroppers can divert attention to the part of the code that may expose many defects, so that the problem of vulnerability at the transmitting end is currently extensively studied. Among the countermeasures studied, the use of loss tolerance is one of the most practical solutions. It assumes few conditions and has been specifically proven. However, with development, most of the current research on RFI-MDI QKD protocol is limited to the assumed perfect preparation state, without considering practical limitations.

Disclosure of Invention

The invention aims to provide a method for distributing a quantum key irrelevant to a reference system and a measuring device with loss tolerance, which considers the influence caused by preparation state defects in an actual scene and has low system complexity.

In order to achieve the purpose, the invention adopts the technical scheme that: a quantum key distribution method irrelevant to a reference system and a measuring device with loss tolerance is characterized in that four-strength decoy states are combined with a loss tolerance scheme to solve the influence caused by state preparation defects in an actual scene, and meanwhile, modulation errors and statistical fluctuation are considered.

Further, a four-strength trap state RFI-MDI QKD protocol is adopted, wherein a signal state mu is only prepared on a Z base, the other two trap states v and w are prepared on the Z base, the X base and the Y base, the probabilities are 0.5, 0.25 and 0.25 respectively, and the rest related probabilities and strengths are optimized according to actual system parameters.

Further, by additionally applying a loss tolerance scheme, the RFI-MDI QKD system only needs to assume that the prepared quantum light is in a two-dimensional state space, and due to the characteristics of the dual independent protocols of the reference frame and the measurement device, the calibration of the reference frame and the side channel leak of the detection section are avoided, thereby simplifying the system requirements.

Compared with the prior art, the invention has the following beneficial effects: compared with the existing RFI-MDI QKD protocol, the invention provides a method for distributing the independent quantum key of the reference system and the measuring equipment with loss tolerance, the method adopts four-strength decoy states, combines with a loss tolerance scheme, considers the influence caused by the preparation state defect in the actual scene, further compacts a theoretical model with the preparation state defect, simultaneously considers the modulation error and the statistical fluctuation, and further promotes the application of the QKD in the actual scene in the practical angle, thereby having good application prospect in the actual quantum cryptography and quantum communication systems.

Drawings

FIG. 1 is a diagram of an experimental setup for validating the method in an embodiment of the invention.

The devices contained in the figure are as follows: laser is a Laser of a transmitting end and a receiving end; IM is an intensity modulator; PM is a phase modulator; BS is 50; FM is Faraday reflector (Faraday-Michelson (F-M) interference ring is composed of FM and PM); ATT is an optical attenuator; EPC is an electronic polarization controller; PBS is a polarization beam splitter; the SNSPD is a superconducting nanowire single photon detector.

Detailed Description

The invention is further explained below with reference to the drawings and the embodiments.

It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure herein. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an", and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.

The embodiment provides a method for distributing a quantum key irrelevant to a reference system and a measuring device with loss tolerance, which solves the influence caused by state preparation defects in an actual scene by adopting a four-strength decoy state and combining a loss tolerance scheme, and simultaneously takes modulation errors and statistical fluctuation into consideration.

First we describe in detail the basic protocol steps of the RFI-MDI QKD protocol in this method:

the RFI-MDI QKD protocol is proposed to avoid the vulnerability of the reference frame to calibrate and detect the generation of side channels in real time. The basic steps include the following:

(1) The sending end Alice and the receiving end Bob modulate a weak coherent source with random phase, and select the strength l and r from the { mu, v, w, o } set, and the corresponding probability is P _l And P _r . For simplicity, in a symmetric system, we can reasonably assume that the selection probabilities of the same intensity are the same。

In this example, the preparation of four intensities is specific, where the signal state μ is prepared only at the Z base, the remaining two decoy states v and w are prepared at the Z base, the X base and the Y base, and the probabilities are 0.5, 0.25 and 0.25, respectively. This brings the advantages that: the signal state only needs to be responsible for key generation, while the two strengths of the spoof state are used to make the parameter estimates. Therefore, when global parameter optimization is carried out, all light intensities cannot be restricted mutually, and the secret key rate can be greatly improved.

In practical QKD systems, a time-phase encoding scheme is typically employed, especially for MDI type systems. In this case, the reference frame Z basis (arrival time) is very consistent between the two users. However, for the X and Y basis, there is a deflection angle β between the phase reference frames. Most of the prior RFI-MDI QKD schemes do not take into account fabrication errors introduced by actual devices, and thus may leave an eavesdropper with a chance to do so. According to the scheme, by adopting the scheme of tolerant loss, not only can the state preparation error be tolerated, but also the scheme is compared with the original six states, and Alice and Bob respectively only need to prepare four states, and the two-dimensional states can be expressed as:

wherein { δ ₁ ,δ ₂ ,...,δ ₈ ,θ ₁ ,θ ₂ ,θ ₃ ,θ ₄ Represents the as-prepared defect, which can be measured by an experimental system. β is the deflection angle between the Alice and Bob reference frames, and the subscripts A and B represent the respective quantum states of Alice and Bob, respectively.

(2) An Untrusted Third Party (UTP) takes the bell measurement after receiving the pulses of Alice and Bob. In this work we consider only | ψ ^- >＝|01>-|10>An event.

(3) After enough data is collected, the count rates are made available to Alice and Bob via the third party's public information

And error rate

Where l and r represent the intensity selected by Alice and Bob, and ξ represents the pairwise combination of basis vectors in { X, Y, Z }.

(4) And (4) performing the steps of parameter estimation, error correction, privacy amplification and the like on Alice and Bob to finally obtain the security key.

The key ratio R estimation method related to the RFI-MDI QKD protocol can be expressed as follows:

wherein e ^-μ Mu is the probability of a single photon when the signal intensity at the emitting end is mu,

is the single-photon counting rate, and,

and

respectively representing the total gain and error rate for the ZZ base. I is _AE Eavesdropping information representing Eve, which can be expressed as:

wherein:

is the single-photon error rate under ZZ base, H ₂ (x) Is a binary Shannon entropy function which can be expressed as H ₂ (x)＝-xlog ₂ (x)-(1-x)log ₂ (1-x). C is an intermediate variable which depends on the single photon error rate based on { XX, XY, YX, YY }:

by adopting a loss-tolerant scheme, it is possible,

can pass through fictional states

And

to determine, i.e.:

wherein

Is the virtual state gain when Alice prepares bit j on the alpha basis while Bob prepares bit s on the chi basis, the lower and upper bounds of which can be estimated by using a decoy state scheme. If a conservative estimate is made, equation (7) can be rewritten as:

in order to make the technical scheme, the purpose and the advantages of the invention more clear, the invention is further described in detail by combining an experimental device and referring to the attached drawings.

With the conventional RFI-MDI QKD protocol, an eavesdropper can divert attention to the portion of the code that may expose many defects. Numerous researchers have conducted research and found that the use of loss tolerance is one of the most practical solutions. It assumes few conditions and has been specifically proven.

Aiming at the scheme, a corresponding experimental system is designed to verify the validity and rationality of the invention content.

As an MDI-QKD type system, both Alice and Bob have the same encoding means, primarily for decoy implementation and state preparation. The first prepared Continuous Wave (CW) laser was chopped by Intensity Modulators (IMs) driven by a 50MHz radio frequency signal with a pulse width of 3ns. In addition, two intensity modulators are used to generate four intensities and increase the extinction ratio of the pulse. An additional Phase Modulator (PM) is used to achieve phase randomization. In the preparation stage of the state, a Faraday Michelson (FM) interference ring is combined with PM to play a key role in phase coding and generate front and rear peak pulse signals. The remaining two IMs select a basis vector by chopping the pre-or post-pulses, which correspond to either the time stamp basis or the phase encoding basis. At this time, the sender can successfully prepare the state corresponding to the formula (1). After the signal is attenuated to the single photon level by the variable attenuator, the pulse is sent to the Charlie end through the optical fiber. At the detection end, an Electronic Polarization Controller (EPC) and optical delays maintain the coherence of the pulses from Alice and Bob. Two Superconducting Nanowire Single Photon Detectors (SNSPDs) record the measurement results of the Bell state for further disclosure, i.e., step (2) in the protocol is implemented. The total efficiency of the detection end reaches 60 percent. And then, the security key can be generated through operations such as parameter estimation, post-processing and the like.

Fig. 1 is a diagram of an apparatus at a transmitting end of the system.

In summary, the invention provides an RFI-MDI QKD method with loss tolerance, the protocol adopts four-strength decoy states to solve the influence caused by state preparation defects in an actual scene, and simultaneously only four states need to be prepared, thereby reducing the complexity of part of systems. The allocation method of the four-strong spoofed state is described in detail in this specification. Meanwhile, in combination with the loss tolerance scheme, the patent specification introduces a calculation and generation mode of the key. Compared with the original processing scheme, the scheme can greatly improve the key generation rate and the transmission distance. In addition, some of the most advanced optimization techniques, such as collective constraints and joint estimation, can be applied to further improve performance.

While the foregoing embodiments have described certain embodiments with further details as to objects, technical solutions and advantages, it should be understood that the present patent specification only describes the QKD system formed by optical fiber components, for example, the methods used in the embodiments of the present invention are also applicable to other on-chip QKD systems or free-space QKD systems, and are not intended to limit the present invention.

Claims (5)

1. A quantum key distribution method irrelevant to a reference system and measuring equipment with loss tolerance is characterized in that the method adopts a four-strength decoy state and combines a loss tolerance scheme to solve the influence caused by state preparation defects in an actual scene, and simultaneously, both modulation errors and statistical fluctuation are considered.

2. The reference frame and measurement device independent quantum key distribution method with loss tolerance of claim 1, characterized in that RFI-MDI QKD protocol of four-intensity spoof states is adopted, where signal state μ is prepared only on the Z basis, the remaining two spoof states v and w are prepared on the Z basis, X basis and Y basis with probabilities of 0.5, 0.25 and 0.25, respectively, and the remaining associated probabilities and intensities are optimized for the actual system parameters.

3. The method of claim 2, wherein by additionally applying a loss tolerant scheme, the RFI-MDI QKD system only needs to assume that the prepared quantum light is in a two-dimensional state space, and due to the characteristics of the reference frame and the measuring device dual independent protocols, is free from side channel holes of the calibration and detection sections of the reference frame, thereby simplifying system requirements.

4. The method of loss-tolerant reference frame and measurement device independent quantum key distribution according to claim 3, comprising the steps of:

(1) The sending end Alice and the receiving end Bob modulate a weak coherent source with random phase, and select the strength l and r from the { mu, v, w, o } set, and the corresponding probability is P _l And P _r ；

Wherein, the signal state mu is only prepared on the Z group, the other two decoy states v and w are prepared on the Z group, the X group and the Y group, and the probability is 0.5, 0.25 and 0.25 respectively; the signal state only needs to be responsible for key generation, and the two strengths of the spoofing state are used for parameter estimation;

by adopting a loss tolerance scheme, state preparation errors are tolerated, and Alice and Bob only need to prepare four states respectively, which are expressed as:

wherein { δ ₁ ,δ ₂ ,...,δ ₈ ,θ ₁ ,θ ₂ ,θ ₃ ,θ ₄ The fabricated defect is represented by beta, which is the deflection angle between the Alice and Bob reference frames, and subscripts A and B represent the respective quantum states of Alice and Bob, respectively;

(2) After receiving the pulses of Alice and Bob, the untrusted third party performs Bell state measurement;

(3) After sufficient data has been collected, alice and Bob get the count rate through the third party's public information

And error rate

Wherein l and rRepresenting the intensity of Alice and Bob selection, ξ represents the pairwise combination of basis vectors in { X, Y, Z };

(4) And Alice and Bob carry out steps including parameter estimation, error correction and privacy amplification to finally obtain the security key.

5. The reference frame and measurement device independent quantum key distribution method with loss tolerance of claim 4, characterized in that the key rate R estimation mode of RFI-MDI QKD protocol is expressed as:

wherein e ^-μ Mu is the probability of a single photon when the signal intensity at the emitting end is mu,

is the single-photon counting rate, and,

and

respectively representing the total gain and the error rate under ZZ base; i is _AE Eavesdropping information representing Eve, which is expressed as:

wherein:

wherein

Is the single-photon error rate under ZZ base, H ₂ (x) Is a binary Shannon entropy function expressed as H ₂ (x)＝-xlog ₂ (x)-(1-x)log ₂ (1-x); c is an intermediate variable which depends on the single photon error rate based on { XX, XY, YX, YY }:

by adopting a loss-tolerant scheme, it is possible,

can pass through fictional states

And

to determine, i.e.:

wherein

Is the virtual state gain when Alice prepares bit j on the alpha basis, while Bob prepares bit s on the chi basis, whose lower and upper bounds are estimated by using the decoy state scheme; conservative estimates are made, and equation (7) is rewritten as:

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